[mesa-users] Too much mesh points

David Arnett wdarnett at gmail.com
Mon Aug 8 11:35:50 EDT 2016

Hi Ehsan,

I think your plot agrees with my point: steep composition boundaries (or
any steep boundaries) change the propagation and reflection of waves,
whether the steepness is real or computational. I wonder whether we can use
Kepler (and company) data to constrain how steep (or shallow) such
boundaries are. We have hydro predictions for the late stages already, but
Kepler only has data for H and He burning. We can extend the hydro
predictions to these stages, but it takes hard work;-(

However, back to your figure: does the base model you feed to GYRE have
steep boundaries? Did you interpolate smoothly or did you "fit with step
functions"? Do a spline fit on the lowest zoning, interpolate to finer
zoning, and compare that. We need to know how the results depend upon the
interpolation/zoning algorithm.  It should be easy (relatively easy) for
you to do this now. We might learn something we need to know. Let me know
what you find!

My dumb prediction (please show me wrong): A smooth interpolation will not
change much when zones are added, but  "step function" rezoning will.

Thanks for your clear reply,

On Mon, Aug 8, 2016 at 4:02 AM, Ehsan Moravveji <e.moravveji at gmail.com>

> Dear Dave,
> Thanks for your insightful remarks; it is always great to hear your words.
> Indeed, nothing fills up the void of "missing physics” in massive star
> evolution, but the physics itself; to be developed, implemented and tested
> against observations.
> Thus, I never plea to increasing number of mesh points, to compensate for
> our lack of knowledge of stellar interiors.
> The reason for tuning the number of mesh is that I pipe MESA output into
> GYRE, for later seismic modelling of beta Cephei and SPB stars.
> Back in 2008, and in preparation for seismic interpretation of CoRoT data,
> an interesting exercise was done among several pulsation code developers,
> and it is published in Moya et al. (2008, Ap&SS)
> <http://adsabs.harvard.edu/abs/2008Ap&SS.316..231M>. I quote from their
> abstract:
> “… *Two equilibrium models with different grids, 2172 and 4042 mesh
> points, have been used, .... Comparing the results for these two models
> illustrates the effect of the number of mesh points and their distribution
> in particularly critical parts of the model, such as the steep composition
> gradient outside the convective core. ...*”
> So, to prepare for modelling Kepler data (which exceeds CoRoT in
> precision), we have to ensure that such numerical issues are better taken
> care of. That is the only reason that I put several mesh adjustment weights
> around "regions of interest”, which is actually one of MESA’s niches.
> If you’re still reading his email with interest, then, I have attached a
> figure I made quite some time ago, showing the influence of meshing in MESA
> on the period spacing of g-modes in SPB models (3 Msun). All used models
> have identical physics (same inlist, same age). The only difference is in
> the meshing: in the first 6 top panels, I only change the mesh_delta_coeff
> (delta) between 1 and 0.02, giving 863 to 47000 mesh points. A visual
> inspection quickly tells how the dips in the period spacing (Delta P) are
> modified. In the latter two (bottom) panels, I use MESA’s mesh refinements
> with a modest mesh_delta_coeff value. Then, the Delta P for the last model
> with 4100 mesh looks “similar” to some of high-resolution models (in the
> observed SPB period range of 1 to 3 days). Then, I stop adding more mesh.
> The Kepler SPB stars (with tens of observable g-modes easily probing the
> near-core environment) are only one among many other applications, where
> going beyond MLT is urgently needed. We’re desperately waiting for it …
> Fortunately, asteroseismology can quantitatively test boundary mixing.
> Thanks again Dave for your motivating email.
> Regards,
> Ehsan.
> On 07 Aug 2016, at 17:46, David Arnett <wdarnett at gmail.com> wrote:
> Hi Ehsan,
> You are asking for more resolution than the physics in MESA can provide.
> MESA is great, but it is only as good as the accepted science we give Bill
> to implement. Mixing-length theory (MLT) fails at convective boundaries (it
> is singular there, and as 3D simulations have shown a boundary layer
> develops, for braking). None of this is in MLT, so we have to use various
> patches to get over this embarrassment. Finer zoning does not capture
> missing physics. I suspect that the default mesh would contain as much
> correct information as the 3,000 mesh points you seek.
> If you wish to do convective boundaries better, you must go beyond MLT.
> --
> David Arnett
> Regents Professor
> Steward Observatory
> University of Arizona
> Facts are stubborn, but statistics are more pliable.  Mark Twain
> Facts do not cease to exist because they are ignored.  Aldous Huxley

David Arnett
Regents Professor
Steward Observatory
University of Arizona

Facts are stubborn, but statistics are more pliable.  Mark Twain
Facts do not cease to exist because they are ignored.  Aldous Huxley
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